Solving Equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the first step in solving the equation 4x + 3 = -5?

Back

Subtract 3 from both sides to isolate the term with the variable: 4x = -5 - 3.

Front

How do you isolate the variable in the equation 4x = -8?

Back

Divide both sides by 4 to solve for x: x = -8 / 4.

Front

What is the solution to the equation 7(2x - 4) = 42?

Back

x = 5.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you simplify the expression 3(b + 5)?

Back

Use the distributive property: 3b + 15.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What is the solution to the equation -11 + 3(b + 5) = 7?

Back

b = 1.

Front

What is the solution to the equation 3r - 5 = 2r?

Back

r = 5.